login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A138545
Central moment sequence of tr(A^4) in USp(6).
2
1, 0, 3, 1, 27, 26, 385, 708, 7231, 20296, 164277, 608565, 4286161, 19021302, 123867107, 617758729, 3862576095, 20774382552, 127548675709, 720773229015, 4401180707397, 25709943020830, 157204921750191, 939751281408962
OFFSET
0,3
COMMENTS
If A is a random matrix in the compact group USp(6) (6x6 complex matrices which are unitary and symplectic), then a(n)=E[(tr(A^4+1))^n] is the n-th central moment of the trace of A^4, since E[tr(A^4)] = -1 (see A138544).
LINKS
Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices, arXiv:0803.4462 [math.NT], 2008-2010.
FORMULA
mgf is A(z)=e^zF(z) where F(z) is the mgf of A138544.
EXAMPLE
a(5) = 26 because E[(tr(A^4)+1)^5] = 26 for a random matrix A in USp(6).
CROSSREFS
Cf. A138544.
Sequence in context: A271128 A271163 A270017 * A271806 A270289 A344037
KEYWORD
nonn
AUTHOR
STATUS
approved